While the selective symmetry operation resembles template matching in the way
it intersects the edge map with its semi-elliptical deformable model, it also
utilizes the principles of symmetric enclosure. Concepts derived from Reisfeld
[37], Sela [42] and Kelly [20] seem to enhance
the template matching process. Symmetric enclosure is used to weight the
response to the contours being detected by template intersection. The
measurement of symmetric enclosure and the projection of edges along the
template normals filter out a variety of inappropriate edge configurations
which do not form adequate contours. These also amplify desired contours that
would fail to trigger template matching. Figure
demonstrates the advantages of the selective symmetry operation.

Figure 2.18:
Symmetric
enclosure versus traditional template matching. (a)
Although these edges trigger many of the template's angular bins by
intersection, they are severely misaligned with the template's normals and
would yield very weak magnitudes when attenuated via
Equation under the selective symmetry operation.
Traditional matching would erroneously register a strong response. (b) This
contour would erroneously trigger a strong template match but not the
selective symmetry operation due to a low measure of perceptual enclosure.
(c) The contour here would erroneously fail to trigger template matching but
will properly register under the selective symmetry operation due to a
strong sense of enclosure around the model's center.

Thus, the selective symmetry operation reliably detects the desired contours
in a manner similar to template matching, with the added benefits of wide
non-circular annular sampling regions, non-circular phase orientation
weighting, and symmetric enclosure calculations. Furthermore, the selective
symmetry operation is a higher resolution blob detector than Sela's symmetry
transform since it keeps track of edge magnitude and gradually attenuates
misaligned edges instead of discarding them. Furthermore the use of more bits
to describe angular bins, edge orientation and edge magnitude provides a more
reliable response.

However, the selective symmetry operation is not tuned for speed and does not
use pre-calculated lookup tables. The symmetry calculations must be repeatedly
evaluated. Thus, it is computationally slower than the symmetry transform.

The selective symmetry detector is not intended to replace the symmetry
transform but to be used in conjunction with it. By applying the selective
symmetry operation in a neighbourhood around peaks in the interest map, we can
refine the output and localize interest peaks more precisely. Furthermore, by
varying the templates used by the operation, we can detect the specific shape
that triggered the interest map around the interest point. Thus, the selective
symmetry operation is applied as a post-processing step after applying the
symmetry transform to improve the location of the peaks of the interest map
and to estimate the contours that generated them.